1 Montgomery Modular Multiplication in Hard- ware

FEI KEMT
Digital circuits are naturally well-suited for implementation of a PRNG because
of their deterministic nature. For implementation of a physical TRNG it is required
to look for a source of randomness inside a circuit. Typical digital circuits include
only a limited range of sources of randomness that we will investigate further.
As we explained already, true randomness is achievable only in generators based
on some physical phenomenon. Anyhow, one of the main objectives of digital sys-
tems designers is to minimise the impact of spurious analogue effects and achieve
perfect stability of the system. Therefore the goal is an optimisation of clock distri-
bution network for wide range of frequencies and a careful design of PCB layout and
power supply network. One can see these contradictory requirements for the system,
when on one side we expect perfectly deterministic behaviour of digital part of the
system, and on other side we look for a high-quality source of truly randomness for
TRNG placed in the same system.
For the sake of security preferred are completely embedded implementations of
RNG. In such case the internal signals of the RNG are not exposed to potential
attacks. However, due to lack of suitable sources of randomness on a given platform
there are designs that propose a use of external discrete components as a source of
randomness while the processing part of generator is implemented in digital part of
the system (e.g. [112]).
5.2.1 Sources of Randomness
The following sources of randomness can be found in the digital devices:
• metastability
• various types of noise
• clock jitter
Although the clock jitter is primarily caused by a noise and therefore it could be
included under the noise, we mention the jitter as a separate category. The TRNGs
based on jitter use techniques different from the ones based on direct sampling of
noise. In addition, the generators sourced by jitter belong to the most popular
designs of TRNGs.
We note that although the sources of randomness are presented separately, it is
generally more difficult to separate them in the technical designs, where all of them
may be present and have influence on randomness source entropy. As an example
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